The problem of the week will return in the Spring 23 semester. We thank everyone who participated this Fall. For the winter break, we suggest reviewing all the problems from the Fall and working on the additional problems posted at the bottom of the provided solutions.

• Problem 7 Solution received from Prof. Vladislav Kargin.

• Problem 6 We have not received any solutions.

• Problem 5 Solution received from Levi Axelrod and Ashton Keith.

• Problem 4 Solution received from Garrett Gramzow, Prof. Vladislav Kargin, and Ashton Keith.

• Problem 3 Solution received from Prof. Vladislav Kargin.

• Problem 2 Solved by Prof. Vladislav Kargin and Ashton Keith.

• Problem 1 Solution submitted by Simon Bange, Ezra Dryer, Garrett Gramzow, Xi Li, Prakash Singh.